The engine computer(PCM) runs the AC, or allows it to run
In the engine compartment fuse box there is an AC relay, PCM turns this relay on and off, when on power is sent to AC compressor, when off power is cut.
PCM monitors 2 switches on the AC coolant lines, cycling switch and pressure switch, both switches need to be closed or PCM won't close AC relay.
Both switches have 2 wires and can be tested with OHM meter, they should have 0 ohms between the 2 contacts, 0 ohms = closed
Compressor clutch could be the issue.
There is an "air gap" issue with some Ford AC clutches.
First see if compressor is getting Voltage at the clutch but still not engaging clutch.
On the compressor are 2 wires one is a Ground the other will have 12volts if AC is on.
Pull off connector and start engine, turn AC on
Use volt meter on the 2 wires, should get 13-14volts with engine running.
If there is no volts then PCM is not closing AC Relay, could be bad relay or a switch is OPEN.
If there is volts then plug wires back in, no need to shut off engine, if compressor clutch is not engaged then could be air gap issue or bad clutch, tap on the front of the clutch with screwdriver handle, if it engages then air gap is the issue, if not then coil could be bad.
You can test clutch coil with ohm meter, shut off engine, the coil is just what it sounds like, a coil of wire, so should be very low Ohms, 3 to 6 ohms, almost a dead short.